17=(x-3)(x+1)

Solution for 17=(x-3)(x+1) equation:

Simplifying
17 = (x + -3)(x + 1)

Reorder the terms:
17 = (-3 + x)(x + 1)

Reorder the terms:
17 = (-3 + x)(1 + x)

Multiply (-3 + x) * (1 + x)
17 = (-3(1 + x) + x(1 + x))
17 = ((1 * -3 + x * -3) + x(1 + x))
17 = ((-3 + -3x) + x(1 + x))
17 = (-3 + -3x + (1 * x + x * x))
17 = (-3 + -3x + (1x + x2))

Combine like terms: -3x + 1x = -2x
17 = (-3 + -2x + x2)

Solving
17 = -3 + -2x + x2

Solving for variable 'x'.

Combine like terms: 17 + 3 = 20
20 + 2x + -1x2 = -3 + -2x + x2 + 3 + 2x + -1x2

Reorder the terms:
20 + 2x + -1x2 = -3 + 3 + -2x + 2x + x2 + -1x2

Combine like terms: -3 + 3 = 0
20 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2
20 + 2x + -1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
20 + 2x + -1x2 = 0 + x2 + -1x2
20 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
20 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-20 + -2x + x2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -2x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -2x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -2x + x2 = 0 + 20
-2x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-2x + x2 = 20

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 20 + 1

Reorder the terms:
1 + -2x + x2 = 20 + 1

Combine like terms: 20 + 1 = 21
1 + -2x + x2 = 21

Factor a perfect square on the left side:
(x + -1)(x + -1) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + -1) equal to 4.582575695 and -4.582575695.

Subproblem 1
x + -1 = 4.582575695

Simplifying
x + -1 = 4.582575695

Reorder the terms:
-1 + x = 4.582575695

Solving
-1 + x = 4.582575695

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = 4.582575695 + 1

Combine like terms: -1 + 1 = 0
0 + x = 4.582575695 + 1
x = 4.582575695 + 1

Combine like terms: 4.582575695 + 1 = 5.582575695
x = 5.582575695

Simplifying
x = 5.582575695

Subproblem 2
x + -1 = -4.582575695

Simplifying
x + -1 = -4.582575695

Reorder the terms:
-1 + x = -4.582575695

Solving
-1 + x = -4.582575695

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '1' to each side of the equation.
-1 + 1 + x = -4.582575695 + 1

Combine like terms: -1 + 1 = 0
0 + x = -4.582575695 + 1
x = -4.582575695 + 1

Combine like terms: -4.582575695 + 1 = -3.582575695
x = -3.582575695

Simplifying
x = -3.582575695

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.582575695, -3.582575695}